Cf: Peirce’s 1870 “Logic of Relatives” • Preliminaries
https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-p…
All,
I need to return to my study of Peirce’s 1870 Logic of Relatives,
and I thought it might be more pleasant to do that on my blog than
to hermit away on the wiki where I last left off.
Peirce’s 1870 “Logic of Relatives” • Part 1
===========================================
https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1
Peirce’s text employs lower case letters for logical terms of general reference
and upper case letters for logical terms of individual reference. General terms
fall into types, namely, absolute terms, dyadic relative terms, and higher adic
relative terms, and Peirce employs different typefaces to distinguish these.
The following Tables indicate the typefaces used in the text below for Peirce’s
examples of general terms.
Table 1. Absolute Terms (Monadic Relatives)
https://inquiryintoinquiry.files.wordpress.com/2021/11/peirces-1870-lor-e28…
Table 2. Simple Relative Terms (Dyadic Relatives)
https://inquiryintoinquiry.files.wordpress.com/2021/11/peirces-1870-lor-e28…
Table 3. Conjugative Terms (Higher Adic Relatives)
https://inquiryintoinquiry.files.wordpress.com/2021/11/peirces-1870-lor-e28…
Individual terms are taken to denote individual entities falling under
a general term. Peirce uses upper case Roman letters for individual terms,
for example, the individual horses H, H′, H″ falling under the general term h
for horse.
The path to understanding Peirce’s system and its wider implications
for logic can be smoothed by paraphrasing his notations in a variety
of contemporary mathematical formalisms, while preserving the semantics
as much as possible. Remaining faithful to Peirce’s orthography while
adding parallel sets of stylistic conventions will, however, demand close
attention to typography-in-context. Current style sheets for mathematical
texts specify italics for mathematical variables, with upper case letters
for sets and lower case letters for individuals. So we need to keep an
eye out for the difference between the individual X of the genus x and
the element x of the set X as we pass between the two styles of text.
References
==========
• Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives,
Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”,
Memoirs of the American Academy of Arts and Sciences 9, 317–378, 26 January 1870.
Reprinted, Collected Papers (CP 3.45–149), Chronological Edition (CE 2, 359–429).
Online:
• https://www.jstor.org/stable/25058006
• https://archive.org/details/jstor-25058006
• https://books.google.com/books?id=fFnWmf5oLaoC
• Peirce, C.S., Collected Papers of Charles Sanders Peirce,
vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),
vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,
Cambridge, MA, 1931–1935, 1958. Cited as (CP volume.paragraph).
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition,
Peirce Edition Project (eds.), Indiana University Press, Bloomington and
Indianapolis, IN, 1981–. Cited as (CE volume, page).
Resources
=========
• Peirce’s 1870 Logic of Relatives
https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview
Regards,
Jon

BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Lyle
I have my old photocopy of a 1973 Bantam edition and see that I have
underlined a good deal in, among other places, Ch 12, and ...'the
world we know is constructed in order [and thus in such a way as to
be able] to see itself]. [ch 12, p 105].
And of course, the construction and the 'seeing itself' operate
within the existence of Forms- but the Forms emerge within/as a
triadic function. That is, the world doesn't operate within the
mechanical dyadic reduction of Observer/Observed, but as noted, the
observer is part of the Form. In Peirce, this relation is one of
mediation , where input data is mediated by the laws within the
'recipient/observer'...to result in a transformation of this input
data to an output 'interpretant'. That is, hydrogen and oxygen
molecules [input] are mediated by the laws-of-physics/chemistry
[observer] to transform into a water molecule.
I also refer to Spencer Brown's 'imaginary' which I compare with
Peirce's mode of Thirdness, i.e., non-local, not-actualized
rules-of-organization.
As for complex adaptive systems, and self-organization - it's a
huge field- and I've used many references in the past.
Edwina
On Sun 16/01/22 6:13 PM , lylephone(a)cox.net sent:
Edwina,
Given your objective, you will find the fundamental source of "the
triad" in the Laws of Form, which ends with the statement: "We see
now that the first distinction, the mark, and the observer are not
only interchangeable, but, in the form, identical." For the answer
to the question of how "self-organizing", i.e., living systems work
you really should start with Illobrand von Ludwiger's monogram on
"The New Worldview of the Physicist Burkhard Heim." Yes, the
mathematics is extremely difficult, but Heim was as good or maybe
better that Einstein in giving a general, but intelligent, audience
explanation of his theory. Von Ludwiger does an outstanding job in
pulling it all together.
One of the things I told the folks on another forum is that whenever
you see the word "tensor" think "form" because that is what they are
in essence. Tensors are multi-compartmented distinctions that have
their own rules that are an addition to the Calculus of Indications
developed by GSB in Laws of Form.
Best regards,
Lyle
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BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Lyle
Thanks for your reply. My interest in Peirce is not with regard to
terms [I am uninterested in terminology] but in his infrastructure of
existential reality; namely, the triad as a networked 'well-formed
formula' along with the three modal categories - that enables matter
to transform from form-to-form within self-organized complex systems.
Edwina
On Sun 16/01/22 4:15 PM , lylephone(a)cox.net sent:
Edwina,
The work of Charles Sanders Pierce is very interesting, but he never
discovered the "imaginary" values of a complete logical system. I am
sure that had he been given a copy of Laws of Form, his reaction
would have been the same as Bertrand Russell's, "This is the book I
wish I had written."
If your focus on Pierce is based on his introduction of new
terminology to describe things, semiotics, and such, then I sincerely
invite you to read Illobrand von Ludwiger's monogram on "The New
Worldview of the Physicist Burkhard Heim." Heim introduced a lot of
new terms because he was describing things no one had thought of
before.
If you want to skip the physics and go to the heart of the matter,
then start with page 81, "The aspect-related Logic for the unified
Description of Body and Soul."
http://heim-theory.com/wp-content/uploads/2016/03/I-v-Ludwiger-The-New-Worl…
[1]
Here is a sample of what you will find there: "The interpretation of
the two additional dimensions in Heim’s theory as coordinates with
qualitative character demanded the alternative logic being expanded
to an aspect-related logic. With his logical method independent of a
specific statement system Heim was then able to make quantitative and
qualitative statements in a unified formal way. This method is called
syntrometry by Heim. It is the combination of different metronic
structures.
"The consequence is, we no longer need to try deriving life
processes or consciousness from physical quantum processes, but you
start from a superior entity that manifests itself in this logic
method, the syntrometry."
What I am working on now is to demonstrate how Heim's "different
metronic structures" are specific Forms that were Indicated by the
Creator for this specific Universe.
Best regards,
Lyle
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I'm quite confused on why people are interested in Laws of Form.
What is LOF trying to do? Is it just rewriting logic or is there something more fundamental e.g. a universal algebraic system?
What does GSB has to do with DNA, or DNA computing?
What does Lou's work in topology has to do with GSB?
What does GSB's theory has to do with knot theory?
What does GSB's theory has to do with quaternions?
How can GSB's theory be used for designing circuits?
What's wrong with Frege?

Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 16
http://inquiryintoinquiry.com/2022/01/15/charles-sanders-peirce-george-spen…
Re: Conceptual Graphs
https://lists.cs.uni-kassel.de/hyperkitty/list/cg@lists.iccs-conference.org…
::: Gary Zhu
https://lists.cs.uni-kassel.de/hyperkitty/list/cg@lists.iccs-conference.org…
<QUOTE GZ:>
I'm quite confused on why people are interested in Laws of Form.
What is LOF trying to do? Is it just rewriting logic or is there
something more fundamental. e.g. a universal algebraic system?
What does GSB has to do with DNA, or DNA computing?
What does Lou's work in topology has to do with GSB?
What does GSB's theory has to do with knot theory?
What does GSB's theory has to do with quaternions?
How can GSB's theory be used for designing circuits?
What's wrong with Frege?
</QUOTE>
Dear Gary,
I am deep in the middle of other work right now,
but here's a smattering of resources relevant to
the relation between Peirce's logical graphs and
Spencer Brown's calculus of indications, at least
so far as the core subjects of boolean functions
and propositional calculus are concerned.
Survey of Animated Logical Graphs
https://inquiryintoinquiry.com/2021/05/01/survey-of-animated-logical-graphs…
As far as the extension to relations and quantification,
I start from where Peirce started in 1870 and follow up
several of his more radical ideas, ones he himself did
not fully develop. That is what I'm doing on the 1870
Logic of Relatives thread.
Peirce's 1870 “Logic of Relatives” • Overview
https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-o…
Regards,
Jon

I’m studying imprecise probabilities which initially works as an extension in Boole’s Laws of Thoughts. It seems like Boole was solving a set of algebraic equations for probabilities where some of the probabilities do not have precise values therefore need to be bounded. Has anyone studied Boole’s algebraic system of probabilities? Is Peirce extending Boole’s algebraic system in his Logic of Relatives?